 So, thank you everybody for being here, and yeah, I'm going to talk about quantum computers. Actually, a very basic introduction of quantum computers. I don't want to scare anyone, so it will be very basic, and my goal tonight will be to give you an idea of it so that maybe I can awaken you some curiosity and you go farther with more formal study of knowledge or what you want to do, you want to maybe play with it online, we will see during the presentation. First of all, like, why this talk right now? Because, yeah, in these days we read, we hear, we see videos on YouTube about quantum computers. We read around the papers about quantum computers, news about quantum computers. We have a lot of companies that are investing in them, like the big ones we know, IBM, the Wave, Google, Microsoft and so on, and right now it's the right moment because everyone is investing in it, the technology, the research is good enough that we feel that we are close to a final product. And also the impact of this product will be big. For example, Morgan study studied that the high-end computing market will double from 5 billion to 10 billion, and that's crazy. So what are quantum computers? Quantum computers are computers that are based on the laws of quantum mechanics. So I thought that to start maybe I should refresh a bit with the difference between classical physics and quantum physics. Well, classical physics is the physics we can use to describe the state of big objects. Let's say it is, it works very good for big objects and less good for small objects. So for small objects, we switched quantum physics that describe them quite good. Quantum physics might work also for big objects, it's just that all the nice properties that bring are not visible. So we need to go in a small place like at the end of this scale and there we see all the nice properties of quantum physics, we can use them and we can make quantum computers. So what are these properties? Let's survive two of them that may be useful for understanding. So for example, in classical physics we know that classical physics is deterministic, so if we have initial condition of a system, we can always calculate the state future in the evolution. Quantum physics is not deterministic, so we can only talk about probabilities. So I can tell you with which probability the system will be in a certain state, but I cannot tell you that for sure it will be. Another difference is that classical physics is observant dependent, so the outcome of an experiment will always be equal. And quantum physics is observer dependent, means that the observer influence the outcome of the experiment. Then some scientists in the past like Feynman said, can we use this property to build a more powerful machine maybe. Then they started to think about the quantum computer. And so to understand it, I thought it would be nice to start with a classical computer and switch to quantum to understand a bit the difference. The classical computer is based on bit, it is the unit of a computer, maybe one of you heard about it, so a bit can be zero or one. It's like a coin, can be tail or can be head. So if I have a bit, I can represent two to the end values. But there's a catch, only one per time, right? So if I have one bit, I can decide if this bit is one or zero. If I have two bit, I need to decide on the first one, let's say it's zero and on the second one let's say one. What's the difference with the quantum bit? The quantum bit, first of all, in real life, it's any two state system that can be, for example, two levels in an atom, like low level and up level, the polarization of a photon, like the horizontal polarization or the vertical polarization. So whatever is two levels, let's go with the atom for today, it's not important for this talk. And the quantum bit has the special properties that can be one, can be zero, but can be also both of them. Like a coin that is rotating and we don't know if it's idle or pale. What does this mean? It means that if I have a bit, I can represent two to the end values, like a classical bit, but this time I can embed, I encode them all in parallel. So if I have one qubit, I can encode zero and one at the same time. If I have two qubit, I can embed and encode all the possible combinations, zero, zero, zero, one, one, zero, one and so on till end. If I have n, I can encode all the possible combination of n, zero and one. What does this mean in numbers? Like, it's crazy, right? I mean, if I have 30 qubits, I can already represent more than one million of states in parallel at the same time. And that's cool. It's cool. But it's not enough. It's not enough. We need to use other properties. Other properties that we need to use is... Oh, sorry. Yeah. I mean, I forgot. Why this happened? Sorry. This happened because of a property that is called superposition, right? And the superposition tells us that the system can be represented as superposition of the basic states. So for example, if I have a coin, the state of the coin can be represented as superposition of zero and one with alpha and beta being the probability of being zero or beta or one. I say probabilities, but take this with care. It's not really like this, but more or less. Another way to see it is like a vector in a sphere that goes from one to zero. And a qubit can have any position of this vector around the sphere. Things that doesn't happen with a classical qubit because the classical qubit can be only one or zero. What does it say before? This is not enough. We need to use other properties. Another property is the entanglement. Or what connection, let's say, if you want to say it. So what does the entanglement do? The entanglement is when two particles or two coins doesn't work with the coins. Are connected in a way that the state of one particle cannot be described independently from the second particle. What does it mean? If I have two coins or particles that are rotating and I don't know the status, but I know that the result should be equal once I observe them. If I observe the first one and it's one, I know automatically that the second one reveals one. It's like they are connected. And the same if I know that the result should be opposite. So they are both rotating. I look at the first one, it's one. I know that the result of the other should be opposite. And then I look at the other one. I already know that it's zero. That's a nice property. All of them are nice properties. But they are not enough to have a powerful quantum computer, right? Because, okay, I mean, we have this massive parallelism, but it's all probabilities. So what do we do with them? I mean, where is the power? The power is in the algorithm. The algorithm is a set of steps, operations if you want to call it, technical language gates, that allows you to manipulate the qubits and brings you to a result. My algorithm is so important because it's thanks to the algorithm that we can exploit these two properties, this superposition and entanglement and get faster to the result, faster than a classical computer. Obviously for certain problems, but this is another long talk. So today I wanted to show you a few gates so that you have the feeling of it and then maybe you can go farther yourself. The first simple gate is the X gate. It's a negation. So if I have zero, I apply the gate, I get one. If I have one, I apply the gate, I get zero. Super simple. Let's go farther. I can apply the gates to two qubits. So if I have two qubits, I can have the C node gates. I check the first qubit. If the first qubit is zero, I don't do anything. If the first qubit is one, I switch the second one. So as you see in the image, if I have zero, zero, nothing happens. Zero, one, nothing happens. One, zero, I switch the second one. One, one, I switch the second one. That's a nice gate. And the last one is the other more gate. This is nice, because if I have a qubit or a coin that has initial state is known like it's zero, I can apply the other more gate and get a superposition. Isn't this cool? Let's start with something that I know. I end up with something that I don't know. Why this is useful? So let's see if I have two qubits. Why it's useful? If I have two qubits, the third zero. And I apply the other more gate, I get the superposition of them. And then the total state is just the multiplication of those two states. Zero, zero, zero, zero, one, zero, and one more. So with applying the other more gate, I get the superposition of all of them. That's cool. Let's start for qubits. And I reach this massive parallelism that I talked about in the beginning. And this goes on. I mean, till n and qubit, and then you have all the possible combination in one state. Then using these gates, I exploit the properties of these other gates obviously, but more complicated one. I exploit all these nice properties of quantum physics. And I get results faster for certain group of problem. So, what I use the quantum computer for. Well, when you study physics, they explain you, hey, factorization, search algorithm. Okay, that's boring, right? So today I wanted to say something funny and I thought to go in a risky field. I know the technical people may not totally agree on this, but, well, you can use them to improve the machine learning algorithm, right? We have an algorithm to improve our learning of our machine. And it's heavy. We need a lot of computational power. But we can exploit this superposition, this massive parallelism, and maybe make it faster. We can try to solve the timing assessment problem. What is it? I have a group of cities and I need to optimize the path between them. And the only way to do this is to compute all the possible combinations and then take the minimum one. So it's brute force. With quantum computers, maybe you can optimize this. There are studies of it. It's a very complicated algorithm. We don't talk about this now. Market prediction. Maybe I can use quantum computer to see correlation in the data that I couldn't see normally with a classical computer. Or to optimize a machine learning algorithm that does market predictions and do better investment. And last but not least, to simulate quantum phenomena. Why? Because that's the reason why the quantum computer was proposed. I mean, try not to say, hey, how do we simulate a quantum phenomena, like an atom or whatever? If we have a classical computer, we need to do approximation. Maybe we can simulate a quantum phenomenon with a quantum device. And that's the reason why that's, I would say, the biggest field for now. And, yes, we still don't have quantum computers. And, okay, maybe I need to finish. We still don't have quantum computers ready and finished at home, I know. We have quantum computers in the cloud and with very few qubits, there are a lot of challenges to have a final quantum computer. So for now, we are very limited. And also for the future, I don't think the idea is to have an end-to-end computer but to have an hybrid, meaning I do a classical input. Then I connect to the cloud. I use the quantum computer to optimize my research or my computation. I go out in a classical way with a single result. That's the most probable future. Obviously, very far future, we may have the full quantum device at home but it's very hard because you need to keep these atoms in a very cold environment because they don't need to interact in the environment. I need to finish, ask me why in case later. So if this talk confuses you, or scared you, don't be worried. I mean, Richard Feynman was the first one to think that quantum mechanics is very hard. People that study quantum mechanics still don't understand quantum mechanics. So no one is pretending you to understand quantum mechanics. But maybe now, having a bit of understanding with a small background, you can just trust physics. You know that it works. You know that there are experiments. You know that there are peer review articles. You just use this property that works and maybe go farther with your acquired knowledge for quantum computer quantum algorithms. And maybe one day you can write yourself your quantum algorithm. And here you find a lot of cool stuff to do so. Also for beginners people. And I'm done. Thank you. So as usual, we have five minutes for the questions. So if someone would like to ask a question, we have people with microphones here. So please raise your hand. Yeah. I can, but it doesn't work. But I can hear you. You can shout. Is it green or red? Try again. I'm trying. Thank you for interesting talk. It was really nice. Question. You said that the quantum computer will rise in the future. If you talk about the first solution when you still use classical input and then the cloud, how far would that be, you think? I'm sorry? How far would be the first solution when not a complete quantum device but perhaps using a cloud with quantum physics? So like there are already, if you go here, you can already play with quantum computers offered by Google, IBM and Microsoft. They are not like, maybe still super powerful. I mean, I don't know the one that Google is doing with NASA. I mean, they have, but the public one maybe is still more simple and you can already play with them. But I got your question. You mean more complicated stuff like I said in the application part. There are people that say that we are five, seven years away from it. But it's predictions. You know, it's all based on the research. The main problem of research, as I said, you need to, for now we cannot put many cupids all together. I think the maximum right now is 50, but please correct me, Google people. Because then you lose currents and the properties I thought at the beginning, you lose them. If these atoms interact with the environment, atoms or cupids interact with the environment. So right now they keep this in very cold environments like few kelvin, very few, almost tear kelvin. And this makes them really kind of isolated from the environment. Not totally, but a bit. And there are studies to improve this. So the limitations kind of physical, how to... Exactly. We still don't have maybe the technology or the knowledge to really have full functional quantum computers without these losing properties in time. For now, this isolation of that on the last very few seconds, so you need all the operations you need to do, you need to apply that fast and then it's finished. So that's the limitation now. Sounds very complicated. Thank you. So someone else would like to have a question? There's one there. Please. Thank you. Wait a second. Thank you for your talk. I mean you said a lot about the opportunities of quantum computing. What about the threats? What do you think about our traditional encryption algorithms? As I said before, the first thing that teaches you in physics in quantum is the factorization stuff. When you will have a quantum computer, you may have algorithms that are able to perform factorization of a number. And now our encryption is based on this theory that you have a very big number and you need to find the two prime numbers that gave it. And this is a very, very hard problem. Quantum computer may do it, but that's not a problem. They are already working on algorithms for encryption and key distribution stuff. So does it mean that the quantum approach also provides new ways of encryption? It probably will provide. I mean I don't know the state of art because I didn't go into encryption topic, but I know that might break the normal one, but the classical one, but I think they will provide a different way to encrypt the atomic. And now there are what I read and studied about. It's this quantum key distribution is when you have a password and you want to distribute the key between two people that are far away and they use the entanglement. This is already a way to overcome the classical problem because then you have two particles that are entangled and if there is some person that look at them, ruin the entanglement, you know that the key is not safe. I mean it's more complicated than this, but I'm making it very short, so I'll try again. Cool. So we have time for one more question. If someone would like. Okay, no question. Thank you. Thank you.